Incline

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Geodesy refers to the directly measured distance between a theodolite or tachymeter and a target point as an inclined distance (also inclined distance , spatial distance or inclined side ) . For further processing it must be converted to the horizontal distance and reduced by other small influences .

If we call the inclined distance s , the horizontal distance d and the zenith distance of the measuring beam z (or the elevation angle h = 90 ° -z) , then applies to short distances

d = s sin (z) = s cos (h)

The formula is only valid for short distances; the influence of the earth's curvature must be taken into account for longer distances . Furthermore, from around 500 m ( earlier in the case of steep sights ), the zenith distance z must be corrected due to the refraction of rays ( terrestrial refraction ), which makes up about a seventh of the curvature of the earth, and the distance reduced to sea ​​level .

When measuring the height , the instrument height of the measuring device and the target height of the measured point (e.g. on the measuring stick ) must also be taken into account.

If you used to determine inclined distances with a tape measure , you could either lay it on the floor (then you need the height difference instead of z ), or you stretched it powerfully as the crow flies (then sag and stretch often had to be taken into account). With the electronic distance measurement by modern total station this effort and extra work is not necessary. From around 100 meters, the air density plays a role for laser or infrared measurements (it reduces the speed of light and apparently extends the distance by around 0.03%), but it is already taken into account in the measuring device today.

Also lock dimensions - with which one local measurements can, for example, of buildings easily control - are actually slope distances. Most of the time, however, the road gradient is low, so that the gradient can not be reduced.

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